The effects of symmetry on the dynamics of antigenic variation

In the studies of dynamics of pathogens and their interactions with a host immune system, an important role is played by the structure of antigenic variants associated with a pathogen. Using the example of a model of antigenic variation in malaria, we show how many of the observed dynamical regimes can be explained in terms of the symmetry of interactions between different antigenic variants. The results of this analysis are quite generic, and have wider implications for understanding the dynamics of immune escape of other parasites, as well as for the dynamics of multi-strain diseases.Comment: 21 pages, 4 figures; J. Math. Biol. (2012), Online Firs

Analysis of symmetries in models of multi-strain infections

In mathematical studies of the dynamics of multi-strain diseases caused by antigenically diverse pathogens, there is a substantial interest in analytical insights. Using the example of a generic model of multi-strain diseases with cross-immunity between strains, we show that a significant understanding of the stability of steady states and possible dynamical behaviours can be achieved when the symmetry of interactions between strains is taken into account. Techniques of equivariant bifurcation theory allow one to identify the type of possible symmetry-breaking Hopf bifurcation, as well as to classify different periodic solutions in terms of their spatial and temporal symmetries. The approach is also illustrated on other models of multi-strain diseases, where the same methodology provides a systematic understanding of bifurcation scenarios and periodic behaviours. The results of the analysis are quite generic, and have wider implications for understanding the dynamics of a large class of models of multi-strain diseases

Cultural factors that affected the spatial and temporal epidemiology of kuru

Kuru is a prion disease which became epidemic among the Fore and surrounding linguistic groups in Papua New Guinea, peaking in the late 1950s. It was transmitted during the transumption (endocannibalism) of dead family members at mortuary feasts. In this study, we aimed to explain the historical spread and the changing epidemiological patterns of kuru by analysing factors that affected its transmission. We also examined what cultural group principally determined a family’s behaviour during mortuary rituals. Our investigations showed that differences in mortuary practices were responsible for the initial pattern of the spread of kuru and the ultimate shape of the epidemic, and for subsequent spatio-temporal differences in the epidemiology of kuru. Before transumption stopped altogether, the South Fore continued to eat the bodies of those who had died of kuru, whereas other linguistic groups, sooner or later, stopped doing so. The linguistic group was the primary cultural group that determined behaviour but at linguistic boundaries the neighbouring group’s cultural practices were often adopted. The epidemiological changes were not explained by genetic differences, but genetic studies led to an understanding of genetic susceptibility to kuru and the selection pressure imposed by kuru, and provided new insights into human history and evolution